Question: A composite function can be written as $w\bigl(u(x)\bigr)$, where $u$ and $w$ are basic functions. Is $f(x)=\log(\sqrt{x})$ a composite function? If so, what are the "inner" and "outer" functions? Choose 1 answer: Choose 1 answer: (Choice A) A $f$ is composite. The "inner" function is $\log(x)$ and the "outer" function is $\sqrt{x}$. (Choice B) B $f$ is composite. The "inner" function is $\sqrt{x}$ and the "outer" function is $\log(x)$. (Choice C) C $f$ is not a composite function.
Composite and combined functions A composite function is where we make the output from one function, in this case $u$, the input for another function, in this case $w$. We can also combine functions using arithmetic operations, but such a combination is not considered a composite function. The inner function The inner function is the part we evaluate first. Frequently, we can identify the correct expression because it will appear within a grouping symbol one or more times in our composed function. Here, we have $\sqrt{x}$ inside parentheses. We evaluate this expression first, so $u(x)=\sqrt{x}$ is the inner function. The outer function Then we take the logarithm of the entire output of $u$. So $w(x)=\log(x)$ is the outer function. Answer $f$ is composite. The "inner" function is $\sqrt{x}$ and the "outer" function is $\log(x)$. Note that there are other valid ways to decompose $f$, especially into more complicated functions.